48

You might try starting this kind of lesson with an assignment where you provide a list of different responses to the prompt "Write a variety of word problems which would require the student to multiply 2.3 by 1.4" and have students (perhaps in groups) arrange and rank them by clarity/mistakes/etc. Instead of having students start by writing their ...


12

A style which I really like is to have all the material on the slide, but have the material which you haven't reached yet in light grey. Then, as you move forward, advance your slides to turn light grey into black. That way, people who really want to see what is coming ahead can do that, but it is clear where their attention should be. Here are some slides ...


9

You might start out by giving them a test in the kind of arithmetic they are supposed to teach. This article in the Guardian from 2010 reported that many primary school teachers in the UK were unable to do the arithmetic required by the primary curriculum. Fewer than four out of 10 of those who sat the test – designed for 11-year-olds – could calculate 2.1% ...


9

Partial answer regarding an approach to fix this problem. First: Don't tell them (criticism), but lead them to find out themselves (insight). Now comes the fun part. Don't let them write just the questions. Have them each write the question on one sheet, and write the correct solution, and a short (maybe single-sentence) explanation for their solution (...


7

Ultimately, I think that this is a matter of taste and presentation style. You should create documents which allow you to present in a way that feels natural to you. My preference (and this is a preference, I have no research to back me up) is to use \pause, \onslide, \only, etc quite liberally. I like to tell a story, which (for me) means having the space ...


2

One technique I've seen used which I like is, for a given topic, to have just all of the parts up to the current one being discussed shown. This way there's no temptation to read ahead since it's not shown, the students can see the previous parts to remind them of what they were (and, if for any reason they didn't read some of it earlier, they can do that ...


2

My preference is to use \pause or similar commands to review parts of slides little by little, but not to the extreme. As you said, if you review too all content at once, students get distracted. Also, too much content on one slide creates a dreadful/boring impression. On the other hand, beamer significantly slows down if you use too much pauses. That's ...


2

I can't answer it in any meaningful way since it varies so much, but what I can offer is what the makers of the AP Calc AB test say: https://apcentral.collegeboard.org/pdf/ap-calculus-ab-bc-course-and-exam-description-0.pdf On pages 27-29, it has a list of topics and pacing Unit (class periods of 45-min) 1 (22-23) 2 (13-14) 3 (10-11) 4 (10-11) 5 (15-16) ...


1

I would suggest taking it easy to start but maybe something like base numeration is a way in here. There is no reason we have to use base 10 and students use of different bases can be very important to understanding operations that require regroupings, and that weird alignment under the typical presentation of multiplication algorithms. One example to check ...


1

I highly recommend the book The Number Sense: How the Mind Creates Mathematics, by Stanislas Dehaene and published by Oxford University Press. Another book that comes to mind is The Language Instinct: How The Mind Creates Language, by Steven Pinker. Both books have had broad impact on scholarship related to your question. As you try to refine your question ...


1

I did a survey with my students, asking them what is their preferred presentation method. Here are the results: 27% preferred the "invisible content", where the content is fully hidden and displays as the lesson goes on. 42% preferred the "transparent content", where the content is transparent and displays as the lesson goes on. 31% ...


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